Mode evolution and nanofocusing of grating-coupled surface plasmon polaritons on metallic tip

Fanfan Lu; Wending Zhang; Ligang Huang; Shuhai Liang; Dong Mao; Feng Gao; Ting Mei; Jianlin Zhao

doi:10.29026/oea.2018.180010

Journals >Opto-Electronic Advances >Volume 1 >Issue 6 >Page 180010-1 > Article

Opto-Electronic Advances
Vol. 1, Issue 6, 180010-1 (2018)

Mode evolution and nanofocusing of grating-coupled surface plasmon polaritons on metallic tip

Fanfan Lu¹, Wending Zhang^1、*, Ligang Huang², Shuhai Liang¹, Dong Mao¹, Feng Gao³, Ting Mei¹, and Jianlin Zhao¹

Author Affiliations

¹MOE Key Laboratory of Material Physics and Chemistry under Extraordinary Conditions and Shaanxi Key Laboratory of Optical Information Technology, School of Science, Northwestern Polytechnical University, Xi'an 710072, China

²Key Laboratory of Optoelectronic Technology and Systems (Ministry of Education), Chongqing University, Chongqing 400044, China

³MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China

show less

DOI: 10.29026/oea.2018.180010 Cite this Article

Fanfan Lu, Wending Zhang, Ligang Huang, Shuhai Liang, Dong Mao, Feng Gao, Ting Mei, Jianlin Zhao. Mode evolution and nanofocusing of grating-coupled surface plasmon polaritons on metallic tip[J]. Opto-Electronic Advances, 2018, 1(6): 180010-1 Copy Citation Text

EndNote(RIS)

BibTex

Plain Text

show less

Abstract

We present a detailed analysis on mode evolution of grating-coupled surface plasmonic polaritons (SPPs) on a conical metal tip based on the guided-wave theory. The eigenvalue equations for SPPs modes are discussed, revealing that cylindrical metal waveguides only support TM₀₁ and HE_m1 surface modes. During propagation on the metal tip, the grating-coupled SPPs are converted to HE₃₁, HE₂₁, HE₁₁ and TM₀₁ successively, and these modes are sequentially cut off except TM₀₁. The TM₀₁ mode further propagates with drastically increasing effective mode index and is converted to localized surface plasmons (LSPs) at the tip apex, which is responsible for plasmonic nanofocusing. The gap-mode plasmons can be excited with the focusing TM₀₁ mode by approaching a metal substrate to the tip apex, resulting in further enhanced electric field and reduced size of the plasmonic focus.

Keywords

electromagnetic field enhancement metal nanostructures plasmonic tip nanofocusing surface plasmon polaritons

$ \frac{{{I_1}({\chi _1}R)}}{{{I_0}({\chi _1}R)}}\frac{{{\varepsilon _{{\rm{Ag}}}}}}{{{\chi _1}}} = - \frac{{{K_1}({\chi _2}R)}}{{{K_0}({\chi _2}R)}}\frac{{{\varepsilon _{\rm{d}}}}}{{{\chi _{\rm{d}}}}} $

(1)

View in Article

$ \begin{array}{l} S{\rm{ = }}\frac{1}{2}\left( {1{\rm{ + }}\frac{{{\varepsilon _{\rm{d}}}}}{{{\varepsilon _{{\rm{Ag}}}}}}} \right)T - \frac{1}{2}\left\{ {{{\left( {1 + \frac{{{\varepsilon _{\rm{d}}}}}{{{\varepsilon _{{\rm{Ag}}}}}}} \right)}^2}{T^2}} \right.\\ {\left. { - 4\left[ {\frac{{{\varepsilon _{\rm{d}}}}}{{{\varepsilon _{{\rm{Ag}}}}}}{T^2} - {m^2}\left( {\frac{1}{{W_1^2}}{\rm{ + }}\frac{1}{{W_2^2}}} \right)\left( {\frac{1}{{W_1^2}}{\rm{ + }}\frac{{{\varepsilon _{\rm{d}}}}}{{{\varepsilon _{{\rm{Ag}}}}}}\frac{1}{{W_2^2}}} \right)} \right]} \right\}^{\frac{1}{2}}}, \end{array} $

(2)

View in Article

$ \begin{array}{l} S = (1/{W_1}){{I'}_m}({W_1})/{I_m}({W_1}), \\ T = (1/{W_2}){{K'}_m}({W_2})/{K_m}({W_2}), \\ {W_1} = {\chi _1}R, \\ {W_2} = {\chi _2}R. \end{array} $

()